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A059555 Beatty sequence for 1 + gamma A001620. 4
1, 3, 4, 6, 7, 9, 11, 12, 14, 15, 17, 18, 20, 22, 23, 25, 26, 28, 29, 31, 33, 34, 36, 37, 39, 41, 42, 44, 45, 47, 48, 50, 52, 53, 55, 56, 58, 59, 61, 63, 64, 66, 67, 69, 70, 72, 74, 75, 77, 78, 80, 82, 83, 85, 86, 88, 89, 91, 93, 94, 96, 97, 99, 100, 102, 104, 105, 107, 108 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Let r = gamma (the Euler constant, 0.5772...). When {k*r, k >= 1} is jointly ranked with the positive integers, A059555(n) is the position of n and A059556(n) is the position of n*r. - Clark Kimberling, Oct 21 2014

LINKS

Harry J. Smith, Table of n, a(n) for n = 1..2000

Fraenkel, Aviezri S.; Levitt, Jonathan; Shimshoni, Michael; Characterization of the set of values f(n)=[n alpha], n=1,2,..., Discrete Math. 2 (1972), no. 4, 335-345.

Eric Weisstein's World of Mathematics, Beatty Sequence.

Index entries for sequences related to Beatty sequences

FORMULA

a(n) = n + A038128(n).

MAPLE

A001620 := proc(n)

        floor((1+gamma)*n) ;

end proc:

seq(A001620(n), n=1..50) ; # R. J. Mathar, Nov 11 2011

MATHEMATICA

t = N[Table[k*EulerGamma, {k, 1, 200}]]; u = Union[Range[200], t]

Flatten[Table[Flatten[Position[u, n]], {n, 1, 100}]]  (* A059556 *)

Flatten[Table[Flatten[Position[u, t[[n]]]], {n, 1, 100}]] (* A059555 *)

(* Clark Kimberling, Oct 21 2014 *)

PROG

(PARI) { default(realprecision, 100); b=1 + Euler; for (n = 1, 2000, write("b059555.txt", n, " ", floor(n*b)); ) } \\ Harry J. Smith, Jun 28 2009

(MAGMA) R:=RealField(100); [Floor((1+EulerGamma(R))*n): n in [1..100]]; // G. C. Greubel, Aug 27 2018

CROSSREFS

Beatty complement is A059556.

Sequence in context: A247779 A243989 A248521 * A186539 A054385 A284773

Adjacent sequences:  A059552 A059553 A059554 * A059556 A059557 A059558

KEYWORD

nonn,easy

AUTHOR

Mitch Harris, Jan 22 2001

STATUS

approved

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Last modified June 20 06:23 EDT 2021. Contains 345157 sequences. (Running on oeis4.)